Smoothed Censored Quantile Regression Process

We approach the globally-concerned censored quantile regression process with a smoothing mechanism for efficient computation. In the low dimensional regime, the regression process is formulated as solving a sequence of smoothed estimating equations (SEE), which can be done via a quasi-Newton method. Coordinatewise confidence intervals of coefficients can be constructed by multiplier bootstrap. In the high dimensional regime, the sparse learning problem is solved by iteratively reweighted ℓ₁-regularized regression, and each ℓ₁-regularized regression is solved by a local majorize-minimize algorithm.

He, X., Pan, X., Tan, K. M., and Zhou, W.-X. (2020). Smoothed quantile regression with large-scale inference. J. Econometrics, to appear. Paper

Koenker, R. and Bassett, G. (1978). Regression quantiles. Econometrica 46 33-50. Paper

Pan, X., Sun, Q. and Zhou, W.-X. (2021). Iteratively reweighted l₁-penalized robust regression. Electron. J. Stat. 15 3287-3348. Paper

Peng, L. and Huang, Y. (2008). Survival analysis with quantile regression models. J. Am. Stat. Assoc. 103 637–649. Paper

Sanderson, C. and Curtin, R. (2016). Armadillo: A template-based C++ library for linear algebra. J. Open Source Softw. 1 26. Paper

Zheng, Q., Peng, L. and He, X. (2018). High dimensional censored quantile regression. Ann. Statist. 46 308-343. Paper